A combined experimental and numerical research study is conducted to investigate the complex relationship between the structure and the aerodynamic performances of an Archimedes spiral wind turbine (ASWT). Two ASWTs are considered, a prototypical version and an improved version. It is shown that the latter achieves the best aerodynamic performance when the spread angles at the three sets of blades are _{1} = 30°, _{2} = 55°, _{3} = 60°, respectively and the blade thickness is 4 mm. For a velocity _{P} values are 0.223 and 0.263 for the prototypical ASWT and improved ASWT, respectively, and the maximum _{P} enhancement is 17.93%. For _{P} values of the prototypical ASWT and improved ASWT are 0.225 and 0.263, respectively, with an aerodynamic performance enhancement of 16.88%. Through mutual verification of the test outcomes and numerical results, it is concluded that the proposed approach can effectively lead to aerodynamic performance improvement.

From 2023 onwards, countries worldwide are emphasizing the reliability of energy supply. The emergence of solar panels, while costly to manufacture, prone to damage, and environmentally polluting, has prompted the search for ways to enhance the efficient use of energy, becoming a new consensus. Renewable energy systems [

Wind turbines typically follow the format of Horizontal Axis Wind Turbines (HAWT) and Vertical Axis Wind Turbines (VAWT) [_{p}). the results show that at _{p} value of the optimal enveloped ASWT is up to 0.502, which is 2.58 times that of the bare ASWT (_{p} = 0.195).

Currently, research on Archimedes Spiral Wind Turbines includes various studies. Chaudhary et al. [

However, these studies are limited to the comparison of the angle changes of several sets of single models and do not fully consider the changes in the angle of system division and the analysis of the regular changes of related parameters. In the process of modification, according to the change law of ASWT performance parameters, the movement of the pressure surface area is caused by the modification of ASWT. Therefore, in addition to the strict division of the inclination angle specified on the helix equation in the physical modeling process, the researchers should also ensure a fixed distance between the pitches to explore the influence of the blade spread angle on the aerodynamic performance of ASWT. This paper proposes a geometric-physical model for measuring ASWT. Firstly, the design method of the ASWT model is introduced. Unlike traditional methods, this approach combines voltage and current test results to characterize changes in power. Subsequently, numerical simulations of ASWT with different structures were considered, and the simulation results were compared with the experimental results. Finally, the experimental and numerical methods used in this paper are summarized and prospected.

The distribution of the structure in this paper is mainly as follows: the

In this study, the aerodynamic performance of a prototypical Archimedes Spiral Wind Turbine (ASWT) with a fixed spread angle and an ASWT with a variable blade spread angle is compared and analyzed. The ASWT with the spread angle corresponding to the best aerodynamic performance is determined. Based on achieving the optimal aerodynamic performance working condition, the noise characteristics of the ASWT before and after modification are experimentally calculated.

A prototypical ASWT was designed using UG NX12.0 software to serve as an effective reference for modeling the aerodynamic performance evaluation and numerical simulation of the ASWT. Firstly, the parameters for blade spreading angle and blade helix angle are determined, with the blade diameter of the prototypical ASWT set at 360 mm, and the helix angle ranging from 0° to 360°. The blade spread angle is independent of the helix angle. As depicted in _{1}, _{2}, _{3}, represents the angle between the blade and the rotating axis, as illustrated in _{3} is positioned at a helix angle of 0°, _{2} at 120°, and _{1} at 240° in the angular displacement plane. Finally, the study of the ASWT is crucial by utilizing the spread angle parameters of three different sets of blades Nawar et al. [_{1} = 30°, _{2} = 45°, _{3} = 60°. Next, we will subdivide the group angles and perform a grouped blade design. As shown in _{1} = _{2} = _{3} = 60° for the three groups of blades, fixed pitch (_{1} = 30°, _{2} = 55°, _{3} = 60° at three sets of blades, fixed pitch (

Items | Prototypical ASWT | Improved ASWT |
---|---|---|

Blade thickness | ||

Number of blades | ||

Aspect ratio | ||

Diameter of wind turbine | ||

1st blade spread angle | _{1} = 60° |
_{1} = 30° |

2nd blade spread angle | _{2} = 60° |
_{2} = 55° |

3rd blade spread angle | _{3} = 60° |
_{3} = 60° |

Fixed-pitch | ||

The diameter of the rotating shaft | ||

Material | SLA | SLA |

The test was conducted in the Key Laboratory of Efficient Energy Utilization of Xinjiang Institute of Engineering (Urumqi, Xinjiang, China). The testing was performed in a low-speed wind tunnel, specifically, the DZS-1400 × 1400/2000 × 2000-I low-speed wind tunnel, which is comprised of an open section (the first test section) and a closed section (the second test section). As the external dimensions of the wind turbine were designed to be that of an Archimedes spiral wind turbine, the aerodynamic performance test was carried out in the closed section of the second test section, as illustrated in

The aerodynamic characteristics of an ASWT are usually described by a set of dimensionless aerodynamic performance curves [

The ASWT test torque is calculated from

The power coefficient ^{−5} kg/m^{3}).

The measurement equipment includes a power analyzer, as shown in

The geometrical model structure of the ASWT was parametrically designed in UG NX12.0 by establishing the Archimedean helix equation. The designed model was imported into Spaceclaim software for area delineation pre-processing, and then imported into ICEM CFD 2020 R2 and ANSYS-Fluent 2020 R2 Meshing software for structural meshing in the stationary domain and non-structural meshing in the rotating domain, respectively. Finally, the meshes of the two regions were overlapped and imported into the ANSYS-Fluent 2020 R2 solver for the steady-state solution.

The ANSYS-Fluent 2020 R2 software provides a feasible approach to establishing a reasonable meshing and calculation for this computational domain. To obtain accurate calculation results, the meshes in the stationary and rotating domains are refined, respectively. The ANSYS-Fluent 2020 R2 solver, which employs the Navier-Stokes equations (RANS) and the Finite Volume Method (FVM), is capable of meeting the requirements for the accurate prediction of flow fields in the stationary and rotating domains. The rotation domain mesh is refined to ensure the accuracy of predicting the flow field. Additionally,

In

The meshing of the complete computational region is illustrated in

In this case, the growth rate of all the blades and the rotating axis boundary is 1.2. The height of the first layer is 2 × 10^{−5} m. The direction of the incoming flow is distributed in the normal direction, so the number of layers of the prismatic layer around the blades is set to 18 to ensure computational convergence, all of which remain unchanged in the mesh independence verification, as shown in ^{+}

No. | Number of CFD cells | Torque coefficient | Correlation error % |
---|---|---|---|

1 | 4543073 | 0.189773 | 1.3407 |

2 | 5321106 | 0.191708 | 0.3348 |

3 | 6276041 | 0.192005 | 0.1803 |

4 | 7667253 | 0.192352 | 0 |

To be able to accurately predict the aerodynamic performance of a prototypical ASWT, the model solution is initially simulated using the RANS equations for the flow field. The numerical solution of the moments is obtained after the convergence of the flow field [

Model constants | Value |
---|---|

α* | 1 |

α | 0.52 |

β* | 0.09 |

β_{i, 1} |
0.075 |

β_{i, 2} |
0.0828 |

σ_{k, 1} |
1.176 |

σ_{k, 2} |
1 |

σ_{ω, 1} |
2 |

σ_{ω, 2} |
1.168 |

Continuity

Momentum

Reynolds stress tensor

_{k} and _{ω} are represent the turbulent kinetic energy generated by the mean velocity gradient down _{k} and _{ω} are represent the turbulent dissipation generated by _{k} and _{ω} mean it is a user-defined source term, _{k} and _{ω} are represent the effective diffusivity defining

The turbulent viscosity is calculated as follows:

First, the steady-state solution is established by setting reference values for inlet velocity, windswept area, air density, and reference chord length to calculate torque and wind power coefficients. Second, the method employs the Coupled algorithm [^{−6}. The detection point at the center of the rotation axis is defined to monitor the trend of the moment change. After about 200 iterations, it is observed that the monitoring value does not tend to be smoothed with the change in the number of iterative steps, and the residual curve steadily decreases to the vicinity of 1 × 10^{−6}, indicating that the convergence condition is reached. The output of the steady-state flow results is torque. The steady-state computational parameter settings are shown in

Parameters | Description |
---|---|

Fluid area | Rectangular area containing the ASWT |

Mesh type | Hexahedral Structured/Tetrahedral Unstructured Structured Mesh |

Number of cells | 6276041 |

Turbulence model | SST k-ω |

Materials (fluids) | Air |

Inlet | Velocity |

Outlet | Pressure |

Cell Grid Area Condition | MRF |

Rotor wall mesh type | No slip-wall |

Residual criteria | 1 × 10^{−6} |

Gradient | Least-squares unit |

Pressure | Quadratic |

Momentum | Second-order |

Turbulent kinetic energy | Second-order |

Turbulent dissipation rate | Second-order |

In this section, the primary focus is on the evaluation of the aerodynamic characteristics of the prototypical ASWT wind turbine and the improved ASWT.

An error analysis of the actual measurement results is also a crucial step. Test errors may arise from imperfections in the test program, personal reading errors, instrument errors, and various other factors. Taylor’s theory is employed for the error analysis of the measurement results. The findings indicate that the relative errors of the torque coefficients at 10 and 8 m/s are 1.44% and 0.90%, respectively, and the errors of the power coefficients at 10 and 8 m/s are 98.56% and 99.1%, respectively.

Here, the relative error is

The prototypical ASWT is initially validated numerically at steady incoming wind speeds of 4, 6, 8, and 10 m/s. _{T} and _{p}, respectively. The results demonstrate a good agreement between the experimental values and the numerically calculated results in the corresponding

The predicted values of _{T} and _{p} were found to be slightly higher than those measured experimentally for the low wind conditions 6 and 8 m/s. To prevent the accumulation of excessive turbulent kinetic energy in the stagnation region, the SST k-ω turbulence model [^{5}, and the flow is in a fully developed turbulent state, the SST k-ω turbulence model alone is sufficient for accurate performance prediction of the ASWT.

However, in the transition region with Reynolds numbers of 1.48 × 10^{5} and 1.98 × 10^{5} at wind speeds of 6 and 8 m/s, respectively, it is more appropriate to use the SST k-ω turbulence model with the Kato-Launder limiter. As shown in _{T} are 0.244, 0.249, and 0.252 at _{T} at 0.260, 0.252, and 0.248 for the corresponding _{P} are 0.219, 0.223, and 0.227 at _{P} value is enhanced by 3.65% when the incoming wind speed is 8 and 10 m/s compared to the incoming wind speed of 6 m/s, and the maximum _{P} value is enhanced by 1.79% when the incoming wind speed is 10 m/s compared to the incoming wind speed of 8 m/s. The experimental results exhibit maximum values of _{P} at 0.213, 0.226, and 0.228 for the same operating conditions at _{P} are enhanced by 7.04% when the incoming wind speed reaches 8 and 10 m/s compared to that at the incoming wind speed of 6 m/s. As shown in

CFD 4 m/s | CFD 6 m/s | CFD 8 m/s | CFD 10 m/s | |
---|---|---|---|---|

0.50 | 4.627 | 22.439 | 74.043 | 181.647 |

0.70 | 4.097 | 21.375 | 67.519 | 163.809 |

1.00 | 3.712 | 19.439 | 60.376 | 154.217 |

1.25 | 3.408 | 17.733 | 55.744 | 136.379 |

1.50 | 3.106 | 15.907 | 49.628 | 124.339 |

1.58 | 2.951 | 15.705 | 43.075 | 120.915 |

1.74 | 2.847 | 12.953 | 41.033 | 104.875 |

2.00 | 2.620 | 10.137 | 37.853 | 71.477 |

Under completely turbulent conditions, the ASWT exhibits unique peak-like curves that are plotted by the dimensionless parameters (_{P}, _{T},

The boundary layer mesh height is specified according to the range of values of the dimensionless number ^{+} to ensure a reasonable range of ^{+} values for analyzing prototypical ASWT wind turbine models. The ASWT generates power by relying on both lift and drag to produce rotational motion. The results of numerical calculations comparing ^{+} < 3 and ^{+} < 1 are shown in ^{+} < 1 is more suitable for the results of the experimental tests than the numerical case of ^{+} < 3.

Under the premise of keeping ^{+} < 1,the improved ASWT is divided into eleven groups of blade models for numerical simulation and comparison. Three groups of the blade spread angles _{1}, _{2}, and _{3} were grouped and numerically analyzed in the simulation. Firstly, the angle of _{2} is discussed basded on _{1} = 30°, _{2} = 45°, _{3} = 60°, and _{2} varies in the ranges of 40°, 45°, 50°, 55°, while _{1} and _{3} remain constant at 30° and 60°, respectively. When _{2} = 55°, the simulated range of _{P} reaches a maximum value of 0.263 when _{2} is 55°, as shown in

Under the same condition of wind speed _{1} on the _{P} value is analyzed, and _{1} varies in the range of 25°, 30°, 35°, and 40°, while _{3} and _{2} are kept constant at 60° and 55°, respectively. A regular change of the data can be found in _{1} varies from the range of 25° to 40° with an initial increase and then a decrease in the _{P} value. At the same time, it validates Nawar et al. [_{1} = 30°, _{2} = 45°, and _{3} = 60° for good aerodynamic performance. It is worth noting that changing the spread angle at the three sets of blades does not have any effect on the range of _{1}, and it also shows that ASWT was characterized by a wide speed range. When _{1} = 30°, the _{P} reaches a maximum value of 0.263. Therefore, it is concluded that the optimum angle of _{1} is 30°. _{3} varies in the range of 60°, 65°, and 70°, and meanwhile, _{1} = 30°, _{2} = 55° are selected to keep the same as shown in _{3} has a more significant enhancement for the ASWT in the _{3} from 70° to 60° finds that the aerodynamic performance in the _{3} as the best.

Finally, it was concluded that the optimum blade spread angle of the improved ASWT was _{1} = 30°, _{2} = 55°, _{3} = 60°. _{P} of the improved ASWT is 0.263 at _{P} value of the improved ASWT is 17.93% higher than that of the prototypical ASWT. In addition,

According to the design prototye, ASWT generates aerodynamic sources that are distributed in three dimensions. Therefore, it is particularly important to analyze the aerodynamic forces on the forward-looking datum. The aerodynamic analysis of the prototypical ASWT shown in _{X} and _{Y} generated in the incoming flow direction are decomposed into the lifting force _{L} and the drag force _{D}, _{X} can be decomposed into _{Lx}, _{Dx}, and _{Y} can be decomposed into _{Lx}, _{Dy}. Therefore, the rotational motion of the ASWT is mainly dominated by _{Y}. It is concluded that during the rotation of the ASWT. The three parts of the blades are arranged in alternating rows of 120°, so that the airflow is uniformly and repeatedly acted on each group of blades under the dominant effect of _{Y}, thus achieving the purpose of power generation.

_{P} reaching its maximum value. The aerodynamic _{Y} value of the prototypical ASWT is 0.70 N, and the aerodynamic _{Y} value of the improved ASWT is 0.84 N. The _{Y} value of the improvement is 20% higher than that of the prototypical ASWT. The aerodynamic _{X} value of the prototypical ASWT is 4.11 N, and the aerodynamic _{X} value of the improvement ASWT is 4.78 N. The _{X} value of the modification is 16.3% higher than that of the prototypical ASWT.

Items | Prototypical ASWT | Improved ASWT |
---|---|---|

Aerodynamic force | _{Y} = 0.70 N |
_{Y} = 0.84 N |

_{X} = 4.11 N |
_{X} = 4.78 N |

In this paper, the study of the velocity flow field and pressure field contours can effectively help to understand the effect of ASWT on aerodynamic performance before and after the modification. At

As shown in _{1} decreases in the range of (35° to 30°) and the blade spread angle _{2} increases in the range of (40° to 45°), as in _{1}, _{2} at the first and second blades. The formation of a corresponding low-pressure region downstream of the blades is conducive to the improvement of the ASWT’s ability to capture wind energy. As shown in

The aerodynamic performance of the prototypical ASWT and the improved ASWT was investigated. Using CFD modeling, a variable angle structure was applied to the ASWT, and the effects of different blade structure changes on the aerodynamic performance of the ASWT under the optimal aerodynamic performance were evaluated. The main conclusions are as follows: The numerical calculations in the operating range of the total leaf tip speed ratio are consistent with the comparison of the test results.

When the airflow through the ASWT reaches a Reynolds number of 2.47 × 10^{5}, indicating fully developed turbulence, with a rotor radius of 35 mm and wind speed of 10 m/s, experimental results show that for incoming wind speeds of 6, 8, and 10 m/s, and TSR of 1.6, 1.6, and 1.5, the maximum values of the _{P} are 0.213, 0.226, and 0.228, respectively.

Based on the flow field analysis, the second blade was found to have a dominant role in influencing the aerodynamic performance of the ASWT in the Z-axis coordinate equivalent plane. The best aerodynamic performance of the retrofitted ASWT was attained when _{1} = 30°, _{2} = 55°, and _{3} = 60°. At a wind speed of 10 m/s, the aerodynamic performance of the improved ASWT is 15.99% higher than that of the prototypical ASWT. The relative errors of the experimental and simulated values are 1.44% and 0.90% for wind speeds of 10 and 8 m/s, respectively, and the torque coefficient measurement accuracies are 98.56% and 99.10%, respectively.

Our research is an effective supplement to the existing research. It has good reference significance, which can provide reference and reference for ASWT performance research, experimental optimization design, and performance prediction. In the future, the airfoil-related parameters will be applied to the ASWT to compare the optimization of its aerodynamic performance and the optimization of the acoustic propagation law.

Turbine sweeping area (m^{2})

_{T}

Turbine torque coefficient

_{P}

Turbine power coefficient

Turbine diameter (m)

Turbine rotational speed (r/s)

Turbine output torque (N.m)

Incoming flow wind speed

Turbulent kinetic energy (m^{2}/s^{2})

Turbine radius (m)

Mach number

^{+}

Non-dimensional wall distance

_{e}

Reynolds number

Measured parameter

Error

_{D}

Obstructive force (N)

_{Dx}

Obstructive force parallel to

_{Dy}

Obstructive force perpendicular to

_{L}

Lift force (N)

_{Lx}

Lift force parallel to

_{Ly}

Lift force perpendicular to

Unfolded angle at the blade (°)

Kinematic viscosity (m^{2}/s)

Dynamic viscosity of the air (kg/m.s)

_{t}

The turbulent viscosity (kg/m.s)

Turbine angular speed (rad/s)

Air density (kg/m^{3})

Turbulent dissipation rate

Archimedes Spiral Wind Turbine

Horizontal-axis wind turbine

Vertical-axis wind turbine

Reynolds-Averaged Navier-stokes

Multiple Reference Frame

Computational fluid dynamics

Relative error

Tip-speed ratio

Finite volume method

None.

This study was supported by the National Natural Science Foundation of China. Project under Grant (Nos. 51966018 and 51466015).

The authors confirm contribution to the paper as follows: supervision, project administration, funding acquisition and writing-review & editing: Yuanjun Dai, Zetao Deng, Baohua Li; study conception and design: Zetao Deng; experiment and data collection: Zetao Deng, Lei Zhong, Jianping Wang; analysis and interpretation of results: Zetao Deng, Lei Zhong, Jianping Wang; draft manuscript preparation: Zetao Deng. All authors reviewed the results and approved the final version of the manuscript.

Since more comparative studies will be conducted in the future, the authors hope that the data will be publicly displayed after the research field and research content are further broadened. The authors do not have permission to share data.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.